Classification of a Class of Solvable Real Lie Algebras by using Techniques in Matrix Theory

TL;DR

This paper classifies a specific class of solvable real Lie algebras, called MD-algebras, using elementary matrix theory techniques, providing a complete understanding of their structure and properties.

Contribution

It offers a complete classification of MD-algebras, expanding the understanding of their structure using accessible matrix theory methods.

Findings

Complete classification of MD-algebras achieved

Identification of key properties of MD-algebras

Elementary matrix techniques effectively applied

Abstract

We give a complete classification of the class of Lie algebras of simply connected real Lie groups whose nontrivial coadjoint orbits are of codimension 1. Such a Lie group belongs to a well-known class, called the class of MD-groups. The Lie algebra of an MD-group is called an MD-algebra. Some interest properties of MD-algebras will be investigated as well. The techniques used in this paper is elementary techniques in matrix theory and available to apply to more general cases.